Goal:
The viscosity of three simple liquids is given over an
extended temperature range. Each data set is analyzed in
order to determine the activation energy (Ea) for viscous flow
of the given liquid.

Prerequisites:
The tasks associated with this assignment can be carried out
with an introductory level knowledge of chemistry.

Resources you will
need:
This
exercise should be carried out within a software
environment that is capable of data manipulation and which can generate
a
best-fit line for an x-y
data set.
You will also be graphing the data along with the
fitted function.

Background:

Viscosity (η)
is a fluid property which indicates how resistant that fluid is to
flow. Highly viscous liquids, like motor oil or molasses,
take much longer to flow from their container than a relatively low
viscosity liquid, like benzene or diethyl ether. To quantify
viscosity, we will imagine our bulk fluid as consisting of a number of
very thin layers. In order for the fluid to flow, a force
will be required to slide these layers relative to one
another. The amount of force (f) required is
assumed to be
directly proportional to the area (A)
of the layers in contact with one another and the
velocity difference (υ)
between the layers. Furthermore, the force is inversely
proportional to the distance (d)
between the layers.
Viscosity (η)
can then be introduced as a constant of
proportionally, yielding a force equation of the form

(1)

Dimensional analysis of equation (1) give SI Units for
viscosity of kg m-1 s-1.
However, the unit that is typically employed in practice is called the
'poise' (P),
where 1 P
= 1 gram cm-1 s-1.
Liquid viscosities
are usually reported in ‘centipoise,’ cP, and gas
viscosity are reported in
‘micropoise,’ μP.

What factors determine whether a given fluid has a high (or
low) viscosity? Certainly the strength
of intermolecular attractions has an influence; nitro-benzene has a
much higher
viscosity than regular benzene because the former is capable of
dipole-dipole
attractions which are considerably stronger than the dispersion
forces of attraction
present in bulk benzene. Other
factors can contribute, such as the size and shape of
molecules. For example, long chain molecules like
polymers are capable of becoming entangled with each other which causes
friction between the hypothetical layers of the fluid which translates
into a
large viscosity.
A number of experimental methods are available for measuring
viscosity. Many are based upon measuring
the amount of time (t)
it takes for a given amount of fluid to flow
through a
thin glass tube or to drain from a vessel that has a small
opening in the bottom. An equivalent measurement is carried on a
fluid of known viscosity. The unknown
viscosity is then calculated using the expression

(2)

where ρ
represents the density of each fluid (which is
usually
measured separately).

Viscosity varies with temperature, generally becoming smaller as
temperature is elevated. This trend occurs because the increased
kinetic motion at higher temperatures promotes the breaking of
intermolecular bonds between adjacent layers. A considerable
amount of research has been carried out in an attempt to understand the
exact
nature of the temperature variation of viscosity. One
relatively simple model assumes that the
viscosity obeys an ‘Arrhenius-like’ equation of the
form

(3)

where A
and Ea
are constants for a given fluid. A
is called the
pre-exponential factor and Ea
can be interpreted as the activation
energy for
viscous flow. Note that this expression
is nearly identical to the Arrhenius equation that describes the
temperature
variation of the rate constant (k)
of a chemical reaction, except
equation (3)
does not have a negative sign in the exponential which causes the
viscosity to
get smaller with increasing temperature.

Equation (3) can be written in the logarithmic form

(4)

If a fluid obeys equation (4), then a plot of viscosity versus
reciprocal absolute temperature should be linear and the slope can be used to
determine the activation energy for viscous flow.

In this assignment, the viscosities of three liquids are given over a
certain temperature range. Each data set is analyzed in order to
investigate whether the liquid obeys the simple Arrhenius model and to
determine the activation energies for viscous flow for these liquids.

Experimental Data:

The following table presents viscosity data for water, ethanol, and
diethyl ether over specific temperature ranges. The data were
obtained from the CRC
Handbook of Chemistry and Physics.

Water

Ethanol

Diethyl ether

Temperature (°C)

η (cP)

Temperature (°C)

η (cP)

Temperature (°C)

η (cP)

20

1.002

0

1.773

-20

0.362

30

0.7975

10

1.466

0

0.2842

40

0.6529

20

1.200

20

0.2332

50

0.5468

30

1.003

25

0.222

60

0.4665

40

0.834

40

0.197

70

0.4042

50

0.702

60

0.166

80

0.3547

60

0.592

80

0.140

90

0.3147

70

0.504

100

0.118

Exercise:

1. Inspect the table and note the relative values of
viscosity for each liquid at a given temperature. Comment on why
the viscosity of diethyl ether is considerably lower than the other two
liquids. What reason(s) can be postulated for why the viscosity
of ethanol is higher than that of water.

2. Enter the data
into an appropriate software environment and, for each liquid, plot the
data in the form implied by equation (4) from above. Determine
the best-fit line for each data set, and plot the original data along
with each best-fit line. Does equation (4) accurately represent
the temperature variation of viscosity for these liquids (note any
discrepancies between your data and the best-fit line)? Does
the model work better for any one of these liquids than it does for
another?

3. Report the activation energy
for viscous flow (Ea) for each liquid in units of kJ/mol and also rank
them from smallest to largest. What is the value of Ea relative to
ambient thermal kinetic energy (given by Ek = RT)?

4. Consult the literature (an internet source will do) and find an approximate strength for a typical (O-H ... O)
hydrogen-bond. Compare the literature value to the Ea values obtained for water and ethanol. Are they of similar
magnitude? What reasons can you postulate for any discrepancy that you may observe between the Ea values and a typical
hydrogen-bond strength?

Suggestions
for improving this web site are welcome. You are
also encouraged to submit your own data-driven exercise to
this
web archive. All inquiries should be directed to the curator:
Tandy
Grubbs, Department of Chemistry, Unit 8271, Stetson University, DeLand,
FL 32720.